Many modern vehicles (e.g., automobiles or aerial vehicles) or mobile computer devices, such as smartphones, tablet computers or other general or special purpose machines, include one or more components for determining information regarding positions, orientations, velocities or accelerations of such vehicles or devices, and for providing navigational advice or instructions based on such information. For example, some vehicles and computer devices include Global Positioning System (or “GPS”) transceivers for determining positions using data received from one or more orbiting satellites, or cellular telephone equipment configured to estimate (e.g., triangulate) a position using signals received from one or more cellular telephone network towers or other network sources.
A GPS-enabled vehicle, device or other system or component may determine its position by interpreting signals that are received from multiple GPS satellites. Where three or more such signals are interpreted, the GPS receiver may be determined to be located at a specific point on the planet to within a certain degree of accuracy or tolerance, commonly on the order of two to ten meters.
Occasionally, position information determined using GPS satellites and GPS-enabled equipment may be inaccurate, irrelevant or unavailable. For example, like any computer device, most GPS-enabled equipment requires an initialization period during which GPS position information obtained or determined by such equipment is unreliable. Furthermore, where an environment includes many natural or artificial obstructions, such as tree limbs, office towers, mountains, walls or ceilings, the receipt of GPS signals by a GPS-enabled device may be delayed or otherwise interpreted as having arrived in an untimely manner.
Moreover, the errors or inaccuracies associated with GPS-determined positions are inherently increased where two or more of such positions are used to determine a relative distance between the positions. For example, where a position of a first GPS-enabled device is determined, and a position of a second GPS-enabled device is determined, each to within two to ten meters of accuracy, a relative distance between the devices calculated based on such positions may be off by as many as twenty meters. The unreliability of relative distances determined based on GPS positions is particularly acute where two or more GPS-enabled devices from which such positions are determined are within short ranges of one another. Where relative distances between two objects are desired, GPS-enabled devices are often ineffective. Furthermore, by itself, a determined position of a GPS-enabled device says nothing about an orientation of the GPS-enabled device, or of a vehicle or other object within which the GPS-enabled device is associated.